Question

Determine whether the equation represents a direct variation. If it does, find the constant of variation. 2y=5x+1

Answer 1

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a direct variation the equation of the line passes through the origin

In this problem we have

$2y=5x+1$ ----> this line not passes through the origin

therefore

The answer is

the equation does not represent a direct variation

Answer 2

It does represent a direct variation.

Direct variation: y = kx
y varies directly with x

Your equation 2y = 5x + 1 is in the form of y = kx but we need to divide out the 2 from 2y so we have the following
2y = 5x + 1
2y / 2 = 5 x/ 2 + 1/2
y = 5x / 2  + 1/2
y = kx
k = 5/2
k = constant of variation = 5/2